Question

How do you solve $ \dfrac{2x}{3}<10 $ ?

Answer 1

Hint: To solve the given equation we will use the basic algebraic operations like addition, multiplication, subtraction, and division. We will first multiply the given equation by 3 then the obtained equation is divided by 2 and then simplifies the equation to get the desired answer.

Complete step by step answer:
We know that inequalities involve the symbols like \[<,>,\le ,\ge \] . To solve an inequality means to find a range or ranges or values that an unknown takes and satisfies the given inequality.
We have been given an equation $ \dfrac{2x}{3}<10 $
We have to solve the given inequality.
Now, by solving the given equation we have to find the value of x as in the given equation x is the unknown variable.
Now, let us multiply the whole equation by 3 we get
 $ \Rightarrow \dfrac{2x}{3}\times 3<10\times 3 $
Now, simplifying the obtained equation we get
 $ \Rightarrow 2x<30 $
Now, let us divide the whole equation by 2 we get
 $ \Rightarrow \dfrac{2x}{2}<\dfrac{30}{2} $
Now, simplifying the obtained equation we get
 $ \Rightarrow x<15 $
Now, on solving the equation $ \dfrac{2x}{3}<10 $ we get the value $ x<15 $ .
It means the value of x must be less than 15 in order to satisfy the given equation $ \dfrac{2x}{3}<10 $.

Note:
 Remember that do not convert the $ < $ sign to $ = $ sign as both are different and it gives the incorrect solution. Avoid basic calculation mistakes and be careful while shifting the terms. Also, we can verify the answer by putting the obtained value in the given equation.